A body of mass 15 kg is hung by a spring balance in a lift. What would be the reading of the balance when (i) the lift is ascending with an acceleration of `2ms^(-2)` (ii) descending with the same acceleration (iii) descending with a constant velocity of `2ms^(-1)`.? Take g = 10 `ms^(-2)`.

Answer

To solve the problem step by step, we will analyze the three scenarios separately, using the concepts of apparent weight and the forces acting on the mass when the lift is moving.

### Given Data:
- Mass of the body (m) = 15 kg
- Acceleration due to gravity (g) = 10 m/s²
- Acceleration of the lift (a) = 2 m/s²

### (i) When the lift is ascending with an acceleration of 2 m/s²:

1. **Identify the forces acting on the mass**:
- Weight of the mass (W) = mg = 15 kg × 10 m/s² = 150 N (acting downwards)
- Apparent weight when the lift is accelerating upwards = W + ma

2. **Calculate the apparent weight**:
- ma = 15 kg × 2 m/s² = 30 N
- Apparent weight = W + ma = 150 N + 30 N = 180 N

3. **Convert to kgf**:
- 180 N = 180 N / 10 N/kg = 18 kgf

**Reading of the balance when ascending**: **18 kgf**

### (ii) When the lift is descending with the same acceleration of 2 m/s²:

1. **Identify the forces acting on the mass**:
- Weight of the mass (W) = mg = 150 N (acting downwards)
- Apparent weight when the lift is accelerating downwards = W - ma

2. **Calculate the apparent weight**:
- ma = 15 kg × 2 m/s² = 30 N
- Apparent weight = W - ma = 150 N - 30 N = 120 N

3. **Convert to kgf**:
- 120 N = 120 N / 10 N/kg = 12 kgf

**Reading of the balance when descending**: **12 kgf**

### (iii) When the lift is descending with a constant velocity of 2 m/s:

1. **Identify the forces acting on the mass**:
- When the lift moves with constant velocity, acceleration (a) = 0.
- Apparent weight = W (since there is no net acceleration).

2. **Calculate the apparent weight**:
- Apparent weight = W = mg = 150 N

3. **Convert to kgf**:
- 150 N = 150 N / 10 N/kg = 15 kgf

**Reading of the balance when descending with constant velocity**: **15 kgf**

### Summary of Results:
- (i) Ascending with acceleration: **18 kgf**
- (ii) Descending with acceleration: **12 kgf**
- (iii) Descending with constant velocity: **15 kgf**